Problem: Solve for $x$ : $x^2 + 8x + 7 = 0$
The coefficient on the $x$ term is $8$ and the constant term is $7$ , so we need to find two numbers that add up to $8$ and multiply to $7$ The two numbers $7$ and $1$ satisfy both conditions: $ {7} + {1} = {8} $ $ {7} \times {1} = {7} $ $(x + {7}) (x + {1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 7) (x + 1) = 0$ $x + 7 = 0$ or $x + 1 = 0$ Thus, $x = -7$ and $x = -1$ are the solutions.